Basic Principles of the CIP-System and Proposals for a Revision By Vladimir Prelog* and Giinter Helmchen Dedicated to the memory of Robert Sidney Cahn (June 9, 1899-September 15, 1981) and of Sir Christopher (Kelk) Ingold (October 28, I893- December 8, 1970) “From Configurational Notation of Stereoisomers to the Conceptual Basis of Stereochemistry” is the title of a lecture [V. Prelog, ACS Symp. Ser. No. 12 (1975) 179) in which the chronologically and alphabetically third member of the CIP-triumvirate discusses the history of the CIP-system. The experience accumulated in the meantime, particularly the efforts to teach computers to use the system as described in 1966 by Cahn, Ingold and Prelog, has shown that certain of its aspects must be more strictly formulated and others modified. Questions dealing with stereoisomers (and stereotopicity), which previously have been treated predominantly in a pragmatic manner, are now discussed in a systematic way. 1. Introduction The last publication in this journal on this topic appeared in 1966[’].Although in general the CIP-(Cahn-Zngold-Prelog) system has served its purpose well, even for special cases not taken into account sixteen years ago, accumulated experience has since shown that there is a need for revision, or at any rate for a more precise formulation of some of its aspects. Contributory to such experience have been our own work, discussions with other colleagues active in this field, and the work of Meyer and C u ~ t e r [on ~’ adaptation of the CIP-system to computer use. Apart from its contribution to the field of stereoisomerism, the CIPsystem has come to serve as the basis for the specification of stere~topicity[~.~] to which it has bequeathed its own shortcomings. This and other aspects unforeseen sixteen years ago have made it necessary now to deal in a systematic way with questions which earlier had been answered on a pragmatic basis only. One serious constraint is necessary in any kind of revision of the CIP rules: previously assigned descriptors should remain unchanged as far as at all possible and should be altered only for compelling reasons, or in problematic cases to which the system has not yet been applied. To this we would add a second limitation: the need for self-restraint in introducing yet more to the already existing surfeit of new stereochemical terms, many of which could well be replaced by established concepts of elementary geometry. We feel that, particularly for educational reasons, economy in coining new terms should be the order of the day. I*] Prof. Dr. V. FYelog Laboratorium fur Organische Chemie, ETH-Zentrum Universitatstrasse 16, CH-8092 Ziirich (Switzerland) Prof. Dr. G. Helmchen Institut fur Organische Chemie der Universitat Am Hubland, D-8700 Wiirzburg (Germany) Angew. Chem. In!. Ed. Engl. 21 (1982) 567-583 Before going into detail concerning our proposals for revision we would like to reiterate the basic tenets of the CIP-system in order to demonstrate its logical construction and self-consistency, notwithstanding the arbitrary nature (mainly for historical reasons) of some of its conventions. We feel that this is necessary in view of certain, in our view, unjustified criticism^"^^^. 2. Basic Principles of the CIP-System 2.1. Stereomodels One of the important aims of static stereochemistry is the specification of the geometry and topography of stereo isomer^^^^. We define stereoisomers as different molecular species of equal constitution (same atomic makeup and atomic bonding), which are separated by intervening energy barriers‘”’. Since for the purpose of the specification of stereoisomers the order of magnitude of these barriers and the physical nature of the bonding, as well as time-dependent properties are immaterial, we assign to molecules rigid stereomodels; geometrical figures, which should contain only the information necessary for that purpose. The model which is our point of departure is a rigid framework of fixed points connected by straight lines. The points define the spatial arrangement of the atomic nuclei and the lines the chemical bonds. 2.2. Chiral, Helical, and Tripodal Four-Point Figures and their Chirality Sense For the description of stereomodels one can advantageously use internal (“chemical”) coordinates, bond lengths, and bond and torsion angles, since they are invariant towards translation and rotation of the model as a 0 Verlag Chemie GmbH, 6940 Weinheim, 1982 0570-0833/82/0808-056 7 $02.50/0 567 whole. Models of nonplanar stereoisomers contain at least one chiral arrangement of four distinguishable points (a chiral three-dimensional simplex) of which two enantiomorphic versions are possible. Since en anti om or phi^^'^^ arrangements are not defined by the absolute values of internal coordinates they have to be specified””. As already showed in 1827, this can be expressed by the algebraic sign of the volume of the corresponding chiral tetrahedron as calculated from the coordinates of its specified vertices in a given Cartesian coordinate system[’’l. There are, of course, many other equivalent procedures for specification of a chiral four-point figure by an algebraic sign. If we start with internal coordinates it is convenient to use instead of Cartesian coordinates of four points the three bond vectors 2, y, Z connecting them. If the bond vectors 2,?, 5constitute a right-handed system, then the algebraic sign of the volume of the corresponding tetrahedron in a right-handed Cartesian coordinate system is positive: if they constitute a left-handed system it is negative. In principle, there are two possible arrangements of three bonds connecting four points: helical and tripodal (Fig. 1). In the helical arrangement the sequence of points ,m 1 4 - + when dealing with stereoisomorphism and stereoisomerism. The chirality sense is unaffected by deformations of the stereomodel; it remains the same provided that the four points do not move into a plane. It is synonymous with the classical concept of “absolute configuration” and at the same time is better defined. Finally, the concept of chirality sense enables one to deal with both tripodal and helical structures within the same general framework. We would like to point out that the distinction between helical and tripodal arrays of four points can serve, according to Gerlach[zol,as the basis for a rational definition of frequently used concepts, such as conformation and configuration, for which no generally accepted definitions exist[”]. Structures and stereomodels which differ in their tripodal arrangements have different configurations, those which differ in their helical arrangements are of different conformation. 2.3. Two-Dimensional Chirality, Heterotopy It is possible to apply the concepts of chirality and chirality sense to spaces whose dimension is either less or more than three. In fact, discussion of two-dimensional chirality can lead to a better understanding of three-dimensional stereoisomerism. The internal coordinates of a planar stereomodel are bond lengths and bond angles. The simplex of two-dimensional space is a three-point figure, the triangle. When this has three distinguishable vertices, it is two-dimensionally chiral, just as the tetrahedron with four distinguishable vertices is three-dimensionally chiral. The simplest stereomodel containing a two-dimensional chiral triangle is the bipodal arrangement of three atom points (Fig. 2), from which the two topologically equivX X Fig. 2. Two-dimensionally chiral simplex: dipodal arrangements of three points, and their bond vectors. Fig. I. Fundamental three-dimensional chiral figures (simplices): a) Helical arrangements of four points, their bond vectors and torsion angles. b) Tripodal arrangements of four points and their bond vectors. can be deduced from the direction of bond vectors as defined by their topological sequence (1 > 2 > 3 > 4 or 4 > 3 > 2 > 1). The bond vector directions are then F= y= 23, F= 34. In the tripodal arrangement the sequence of three topologically equivalent points A, B, and C and the bond vector directions must be defined by a non-topological criterion i. e. by conventional rules, for example A > B > C andx=TA,,G=%, i=xd. In chemistry instead of algebraic signs, expressions such as “right” and “left” or synonymous words and descriptors are used: these, as well as the algebraic signs, signify the chirality sense of that arrangement, a useful concept - - 568 c, alent arrangements, A and B, have to be differentiated by conventional rules. In two-dimensional space such an arrangement can exist in two enantiomorphic non-congruent versions which, however, become congruent in three-dimensional space by rotation. Their enantiomorphism is due to the fact that in two-dimensional space they are “orientated”. In three-dimensional space their two-dimensional chirality is manifested by the fact that a chiral triangle has two distinguishable facesfzz1. In an analogous way to three-dimensional tripodal arrangements it is possible to specify two-dimensional enantiomorphic models or the faces of chiral triangles by the algebraic sign of the area calculated from the Cartesian coordinates of their vertices, or through the algebraic sign of the vector product f = y x I of the two bond vectors I and y’ (Fig. 2). The plane which contains a two-dimensional chiral simplex divides the three-dimensional space into two distinAngew. Chem. Inf. Ed. Engl. 21 (1982) 557-583 guishable half-spaces, which can be specified by the algebraic sign (or by a corresponding descriptor) of the adjacent face of the chiral triangle. Atoms, ligands, and other objects which are located within such distinguishable halfspaces have been termed heterotopic by Mislow and Ra- 2.4. Factorization of Complex Stereomodels into Stereogenic Units Non-planar stereomodels with chiral regions containing more than four connected points can be factorized into four-point regions which can be either tripodal or helical. However, factorization down to regions of four directly connected points is performed only in the case of helical arrangements. For historical and practical reasons, stereomodels which contain three-dimensionally chiral tripodal as well as two-dimensionally chiral dipodal regions are subdivided into units containing more than four or three atoms, respectively, which following a suggestion by M c C ~ s ~ a nwe d ~term ~ ~ “stereogenic units”. It is essential for such a unit to be composed of an achiral core (atom or a skeleton of atoms) with distinguishable ligands, whose constitution-preserving interchange leads to a stereomorphic figure. 2.5. Chirality Elements: Stereogenic Units of the CIPSystem In this paper we wish to restrict ourselves to proposals for revision of the CIP-system concerning stereoisomers with atoms having no more than four ligands. However, subject to appropriate modification, these proposals will also be found applicable to an eventual revision of the rules specifying stereoisomers containing atoms of higher ligancy. For stereomodels of molecules with at most tetraligant atoms, three types of tetrahedral stereogenic units (three chirality elements) are used in the CIP-system: the chirality center, the chirality plane, the chirality axis, and the analogous pseudoasymmetric units. These we shall discuss and analyze as far as the stage of elementary tripodal and helical regions. Apart from these we shall also consider as stereogenic units planar diastereomorphic arrangements of four ligands of planar tetraligant atoms or double bonds which are commonly described as ~is,trans-isomers~~~~. 2.5.1. Chirality Center: The Tetrahedral “AsymmetricAtom” Among three-dimensional stereomodels with more than four points we shall first discuss the five-point figure shown in Figure 3. This is in fact the model for tetrahedral atoms with four distinguishable ligands, which are of overriding importance in organic stereochemistry. A five-point figure of this type can be converted in four different ways into tripodal four-point figures by omission of one conventionally chosen ligand atom point and its bonds. The chirality sense of each of the four-point figures thus obtained would define unambiguously that of the five-point figure. There is, however, a fifth possibility of mapping such a Angew. Chem. In[. Ed. Engl. 21 (1982) 567-583 Fig. 3. Chirality center: enantiomorphic tetrahedral “asymmetric” atoms, corresponding T,-tetrahedra, and their bond vectors. five-point figure onto a homomorphic complementary four-point simplex. In this, the topologically unique central atom point and its four bonds are omitted, and the remaining four points are placed at the vertices of a regular tetrahedron with point symmetry Td1261. The resulting fourpoint model, unambiguously derived from the original five-point model, is in fact the “asymmetric atom” of Le Be1 and van? H o ~ and , at the same time the “chirality center” of the CIP-system. By such a conversion of a chiral five-point figure into a four-point stereogenic center, considerable simplification of the specification process is achieved. Moreover, the concept of the “asymmetric atom” is so deeply rooted in the mind of the organic chemist that a specification system based on more fundamental tripodal four-point units would have had little chance of acceptance. In the CIP-system, even a chiral tripodal triligant atom is converted into a tetrahedral one by adding a “phantom” atom. If the directions of the bond vectors are determined in the conventional manner, then the algebraic signs specifying corresponding tripodal and tetrahedral systems are the same. Such a conversion has the advantage of making it possible to specify the chirality sense of both tripodal four-point models of triligant atoms and of tetrahedral five-point models of tetraligant atoms in an analogous manner. 2.5.2. Chirality Plane and ChiraliQ Axis: n e i r Specification Based on Preferred Helical Regions To specify the chirality of certain stereoisomers which do not possess centers of chirality (stereoisomeric allenes, atropisomeric biphenyls and ansa-compounds) two additional stereogenic units were introduced in 1956: chirality planes and chirality axes. Figure 4 shows two enantiomorphic five-point figures which are fundamental for representing a chirality plane. In each there is a planar two-dimensionally chiral trigonal atom X, with its proximal atoms or ligands A, B, Y and an additional atom 2 connected to Y and lying outside the ABY plane (chirality plane). Such figures can be mapped unambiguously onto four-point simplices. As pointed out in 1972[61one can omit the planar trigonal atom X and its three bonds and then connect the remaining four atompoints with straight lines. This will lead to the formation of a tetrahedral model of point symmetry C, with two topologically equivalent vertices which have to be differentiated by conventional rules in order to obtain a tetrahe569 A A A Fig. 4. Chirality plane: enantiomorphic five-point figures, corresponding C,tetrahedra, and preferred torsion angles A-X-Y-Z. dral stereogenic unit, which is then specified in the usual way. In an analogous manner Figure 5 shows the enantiomorphic figures needed to represent a chirality axis: two nonplanar combinations of planar-trigonal atoms Zl and Z2 with their respective proximal ligating atoms. Such a six-point figure can likewise be mapped unambiguously onto a four-point simplex, a tetrahedron with point symmetry D2d,by omitting atoms Z I and Zz and their bonds followed by interconnecting the remaining four ligand atom points by straight lines. If the ligand atoms occupying the topologically equivalent positions are distinguishable, the resulting figures are representations of tetrahedral stereogenic units, which again can be specified by an algebraic sign in the same way as the other two chirality elements. The line of intersection of the two planes of the trigonal atoms constitutes an axis, hence this stereogenic unit was termed “chirality axis”. aA .’ A .. B are in fact atropisomeric conformers, their specification via the algebraic sign of a preferred torsion angle is particularly appropriate (cf. [”I). Between points X and Y in a chirality plane and points Z, and Zz in a chirality axis it is possible to insert various linear atom-sequences (e.g., =C=, -C=C-) which thus do not influence the specification process. An example of practical significance is that of the chiral allenes containing the linear grouping =C=. The fact that there are molecules with several chirality planes or axes has been mentioned previously[’]. If such stereogenic units are interdependent, then of the possible unambiguous specifications the one chosen should be in accord with Einstein’s advice: “Keep it as simple as possible but not simpler than that”. A multitude of redundant will only confuse rather than elucidate. In case of doubt one should clarify the affiliation of a descriptor by giving the systematic numbering of an appropriate atom, as is customary for differentiating several chirality centers or double bonds; and this atom should advantageously be that among those termed z,,Z2 or X or Y, with the lower systematic number. Among stereomodels with more than six atoms we should briefly mention a seven-point figure comprising a planar trigonal and a tetrahedral atom (Fig. 6). This can be U Fig. 6. A seven-point figure, the corresponding chirality plane, and the preferred torsion angle. BA A ...” B unambiguously mapped onto the five-point figure shown in Figure 4, by the choice of one of three topologically equivalent ligands of atom Y or, in other words, it can be treated as a plane of chirality. The choice of the ligand has to be made in accord with criteria derived from the specification of conformation^^"^. Fig. 5. Chirality axis: enantiomorphic six-point figures, corresponding D2,,tetrahedra, and preferred torsion angles A-ZI-Z2-A. 2.5.3. “Pseudoasymmetric” Stereogenic Units It had previously been recognized[” that planes and axes of chirality can also be specified by the algebraic sign (or the corresponding descriptor) of the torsion angle of a helical array of four atoms chosen by a conventional rule. We now suggest that this simple and unambiguous method should be applied generally in place of the less convenient specification procedures based on tetrahedral simplices. For chirality planes the preferred sequence of atoms is A-X-Y-Z (Fig. 4), and for chirality axes A-ZI-Z2-A (Fig. 5), as already proposed previously. Since stereoisomers with chirality planes and chirality axes The concept of the stereogenic unit comprises not only the elements of chirality mentioned so far, but also the analogous elements of pseudoasymmetry : pseudoasymmetric centers, planes, and axes. These always exhibit two ligands which differ only in their topography, i.e. which are enantiomorphic. In a tetrahedral stereogenic unit such ligands are situated within heterotopic half-spaces ; the chirality sense of such enantiomorphic ligands and of the half-spaces can be combined in two geometrically different ways [(+ +, - -) or (+ -, - +)I. This leads to two geometrically different models and to two diastereomers. Formally, such stereoisomers can be specified analogously to those comprising chirality elements with four 510 Angew. Chem. Inc. Ed. Engl. 21 (1982) 567-583 distinguishable ligands. In contrast to the algebraic sign (or corresponding descriptor) of a chirality element, the algebraic sign of a pseudoasymmetric unit obtained in this way is reflection invariant, because diastereoisomerism is based on a geometrical property. Upon reflection, the chirality sense of both enantiomorphic ligands and their halfspaces are reversed; the two inversions cancel each other out. 2.5.4. The Two-Dimensionally Chiral Triligant Atom. TwoDimensional Diastereomorphism:“Geometrical” Isomerism A planar four-point figure (Fig. 7a), representing the model of a triligant central atom with three distinguishable ligands, can be unambiguously mapped onto a regular triangle in which the central atom and its three bonds have been omitted. This gives the model of the planar “two-dimensional asymmetric atom”, analogous to the tetrahedral “asymmetric atom”. Previously we showed how one can change the model of a tripodal array into a tetrahedral stereomodel by adding a “phantom” atom: in the same way a bipodal array can be transformed into a trigonal “two-dimensional asymmetric” atom. A x A A U xB I .A Fig. 7. a) Two-dimensionally enantiomorphic trigonal “atoms” and their bond vectors. b) Two planar diastereomorphic six-point figures composed of two trigonal two-dimensionally chiral atoms: cis-trans isomerism. As indicated in Section 2.3, enantiomorphic “two-dimensional asymmetric atoms” are congruent in three-dimensional space but non-congruent in the plane because Angew. Chem. Inl. Ed. Engl. 21 (1982) 567-583 of their different “orientations”. From two such orientated “two-dimensional asymmetric” atoms two pairs of planar figures can be constructed: one from two differently and one from two equally orientated atoms. Two pairs are diastereomorphic not only in two-dimensional but also in three-dimensional space (Fig. 7b). They are interconvertible by a constitution-preserving interchange of two ligands. A planar combination of two two-dimensional chiral simplices thus represents a stereogenic unit by definition. The two diastereomorphic figures just mentioned are models of cis-trans isomers containing planar tetraligant atoms or double bonds. 2.6. Differentiation of Ligands To establish the chirality sense of a stereogenic unit it is necessary to determine the rank of its ligands by comparing their properties. Since ligands can differ in several types of properties and the rank of ligands must be determined by a single property, this requires a clear-cut hierarchy of relevant properties and an unambiguous prescription for the order in which they are compared. Moreover, the comparison must be performed in a finite number of steps[”’. The properties used in the CIP-system for differentiation of ligands (see Scheme l) can be divided into material and structural. Material properties are atomic number and (with isotopes) mass number, whereas structural properties include those based on topology (connectedness), geometry, or topography (cf. Section 2.lI9]). Material and topological differences, which in organic chemical usage are termed constitutional differences, are considered first, followed by geometrical differences (either two- or three-dimensional ligand diastereomorphism); topographical differences (ligand enantiomorphism) are treated last. The relative status of the three types of properties is apparent from the sequence (top to bottom) shown in Scheme 1. I constitutional (material and topological) I I geometrical (diastereomorphic) 1 topographical (enantiomorphic) 1 1 I reflectionvariant 1 I Scheme I. Hierarchical order of ligand properties. It is essential to examine the relevant properties of ligands in the hierarchical sequence outlined-exhaustively for each type-before proceeding to the next lower rank. This can be formulated also in the following way: equality with respect to a certain type implies equality relative to that of the higher but not lower rank. For example, geometrically equivalent ligands must be equivalent topologically but can be different topographically. The importance of 571 the precept was recognized only after 1966; nonetheless the Sequence Ruled’] as originally formulated did already follow the correct hierarchical order, a fact that was due to pragmatic recognition of the consequences of not following such an order in a number of cases (see examples (21)-(23) in [‘I). In spite of this, several cases have since been found where the CIP-system appeared to fail because geometrical and topographic properties had not been properly kept apart. In fact, differentiation is always feasible so long as one keeps in mind that differences in topography are based on the reflection-variant enantiomorphism of two ligands, i. e. on their chirality sense, whereas all other properties, geometrical and constitutional, are reflection-invariant. Here it is advisable to point out that a relevant property of a particular ligand used for specification must not be based on its relationship to the stereogenic unit to be specified. This caveat has been discussed in [‘I with special reference to the configuration of the inositols. Finally it should be pointed out that two ligands which are ordinarily equivalent but heterotopic, and thus chemically and physically distinguishable, are of the same rank order: their heterotopy alone is not a sufficient distinction criterion for determining their order of precedence. hedral stereogenic unit is shown advantageously in such simplified digraphs by using Fischer projections. 6 OH 5 H h2=, a) b) C) Fig. 8. a) A constitutional formula in which the configuration of stereogenic atom C-3 is represented by Fischer projection. b) Complete hierarchical digraph of a. c) Simplified hierarchical digraph of a. In the case of an acyclic molecule containing several stereogenic units the hierarchical digraphs of all these units are derived from one and the same non-directed molecular graph (Fig. 9). 3. Hierarchical Digraphs So far we have consistently used the term ligand, without defining it. Its meaning is quite clear in the case of monodentate ligands. On the other hand, for polydentate and cyclic “ligands”, especially as parts of polycyclic structures, the term appears to lose its clear connotation. This can be rectified by converting the polydentate and cyclic ligands into equivalent acyclic structures: their hierarchical digraphs. The hierarchical digraph of the whole stereogenic unit is a directed chromatic acyclic graph, a “tree-graph’’ representing the connectedness (topology) and make-up of atoms: its edges, originating from the root of the treegraph-the core of the stereogenic unit-point towards the branch ends. 3.1. Hierarchical Digraphs of Acyclic Molecules The non-directed graph of an acyclic molecule is obtained from its constitutional formula by addition of duplicate and phantom atoms. The digraph of a stereogenic unit within this molecule is then obtained by assigning directions to the edges, starting from the core and pointing towards the branch ends (Fig. 8). Frequently it is not only sufficient but also advantageous, especially with larger molecules, to use simplified instead of complete hierarchical digraphs. In these simplified versions the nonrelevant hydrogen and phantom atoms are omitted and carbon atoms replaced by their systematic numbering. In developing such a graph one need only proceed to the extent of determining the rank order of all ligands. The spatial arrangement of the proximal atoms of the core of the tetra572 0 0 k t 0 0 I 0 OK0\ 0’ 0 0 t I T ‘o H LO Fig. 9. An acyclic molecule: derivation of the hierarchical digraphs of both stereogenic atoms C-2 and C-3 from the same molecular non-directed graph. 3.2. Hierarchical Digraphs of Cyclic Molecules In order to transform the constitutional formula of a cyclic molecule into an acyclic “tree-graph’’ all rings have to be opened in such a way that the resulting acyclic graph contains all the necessary but no redundant information. This procedure has so far not been properly described, and we shall do so in the following sections. 3.2.1. Stereogenic Units with Pobdentate Ligands In order to obtain the acyclic digraph of a stereogenic unit the n-dentate ligand is transformed into n monodentate ligands, by leaving intact in each case one bond with the core and breaking the remaining n- 1 bonds. At each end of n branches thus obtained a duplicate atom of the core is attached (as in the case of broken multiple bonds) (Fig. 10). Angew. Chem. Int. Ed. Engl. 21 (1982) 567-583 3 .Cp0 3 I 1 \ 1 4 8 1 '/ O \ 7\ / '6 3 \O 1-2-3 1 \ \ / 7 6 \ \ 8- 9-1-5 4- 3 0 ' /l 5-6- 4-5 t 0 ' 1-6-7 3-0 5 \ 1 */ 7-8-1 \O Fig. 12. Hierarchical digraph of a ligand which includes branching due to a bicyclic ring system. I P\, 7 mentioned previously, whereas the digraph of the latter may be derived from the same or from a different non-directed graph, depending on the position of the stereogenic units relative to the ring (see Fig. 13). 1'6 8 I 9 I 1 "0 Fig. 10. Hierarchical digraph of a stereogenic atom with two bidentate ligands. 0,5 rh 3.2.2. Stereogenic Units with Ligands Containing Rings In ligands of a stereogenic unit containing rings these are opened twice after the first ring atom encountered from the core: one bond remains intact and the other is broken; a duplicate of the first encountered ring-atom is attached at the end of the two branches thus obtained (Fig. 11). If the first-encountered ring atom of the ligand turns 4 t t 0 0'4 0 5 ' 6\ 2--1-2-&4< IJ 0. 1' 5 I H .4 a) 1 \ 4 \ 0 1 5 3 \t 4 2 Kt 7/ \ / 2 4 t/ 3 1 / 2 / .it' 5 / / 3 3 5 0 \ 6 \ 4 5 Fig. 1 1 . Hierarchical digraph of a stereogenic atom with two cyclic (threeand four-membered) ligands. out to be the quaternary common atom of a bicyclic system, one of the three ring bonds is kept intact and the other two are broken. Three branches of the tree graph, which are provided at their ends with requisite duplicate atoms, are therefore produced (Fig. 12). A characteristic difference between hierarchical digraphs of stereogenic units in acyclic and cyclic molecules is that in the former the non-directed graph is the same, as Angew. Chem. Int. Ed. Engl. 21 (1982) 567-583 b) Fig. 13. Hierarchical digraphs of two cyclic molecules with two stereogenic atoms each: a) both digraphs derivable from the same molecular non-directed graph, b) each digraph requiring its own molecular non-directed graph. 3.3. Examination of Hierarchical Digraphs. The Precedence of Atoms as a Result of their Topology To establish the order of precedence of ligands, their atoms are rearranged in such a way that their rank is ap573 parent both from their topological distance (number of bonds), from the core of the stereogenic unit, as well as from their evaluation by the sequence rules. Atoms of equal topological distance can be said to lie in the same sphere. Atoms occupying the n-th sphere have precedence over those in the (n + 1)th sphere. The ranking of each atom within an n-th sphere depends in the first place on the rank of the atom within the (n- 1)th sphere to which it is bonded, and only then on its rank according to the sequence rules. The first sphere is occupied by the proximal atoms p, p‘ (Fig. 14). Those in the second sphere are numbered 1,2,3,.. ., and those in the Those atoms in the n-th sphere which are of equal rank with respect to those in the (n- 1)th sphere to which they are bonded are graded by means of the sequence rulesand these are applied exhaustively in turn: first the entire hierarchical graph is examined by sequence rule 1. If a clear precedence over other ligands can be established, the examination of that particular ligand is concluded. If ligands remain whose rank is not provided by sequence rule 1, then one uses sequence rule 2, once again exhaustively, and so forth. While this procedure is in accordance with precepts published earlier“] it now makes clear, we hope, that a rank established for a sphere nearer to the core remains valid with respect to atoms in more distant spheres (Fig. 15). 4. Descriptors Fig. 14. Rank order of two ligands with proximal atoms p and p’. third sphere 11, 12, 13, 21, 22, 23 ... etc.; the smaller the number, the higher the relative ranking. Br H CI I Br + OH \ / 6 / 1 H CI-,~ 4 Fig. 15. Illustration of the precept that a branch rank, once determined, has subsequent priority: to determine order of sequence of both cyclohexyl groups the rank order 3-Br>3‘-CI is used, and not 5’-1>5-CI because the former atom-pair is attached to branches of higher rank due to 2-F and 2-F’, respectively. 574 In principle, one could specify stereoisomers by the algebraic sign of their stereogenic units as shown in Figures 1 to 5, wherein vector directions are defined as proceeding from points of lower to those of higher precedence. There are, however, good reasons for using letters (descriptors) instead of algebraic signs for such specification: 1) ( + ) and ( - ) have for long been employed to signify the direction of rotation of polarized light of enantiomers, 2) use of these signs does not clearly establish whether they are reflection-variant or -invariant (cf. Section 2.5.4), 3) use of a multitude of algebraic signs is also not conductive to oral or written transmission of information. Scheme 2 gives a complete summary of descriptors employed in the revised CIP-system, wherein reflection-variant descriptors are marked by capital and -invariant descriptors by lowercase letters. The descriptors are: Re,Si”’b’;re,sialb);R , S ; r,sc);P,Md’;p,m‘’. Abbreviations for descriptor pairs: lk, Lk, I for like, ul, U1,u for unlike. ReRe, SiSi= Ik‘); ReSi=uI”; reRe, siSi= Lkg); reSi, siRe=Ulg’; R R . S S , MM, PP, RM, S P = I ; RS, MP, RP, SM=u. re, si have been suggested by Han~on[’~ for specifying the lateral faces of planar chiral trigonal atoms. No suggestions were put forward for differentiating between reflection-invariant and -variant faces. We have used Re, Si, re, and siL6I to specify two-dimensional stereogenic units and heterotopic half-spaces; here, reflection-variant units were denoted by Re, Si, and -invariant units by re, si. R , S, r, and s were first introduced in [*I. P and M were suggested in [’I and are based on a convention put forward in I”]. p and m are suggested in this paper as symbols for the specification of reflection-invariant “pseudo-asymmetric axes” and “pseudo-asymmetric planes”. It might be possible to specify cis-trans diastereomers of compounds containing planar tetraligant atoms or double bonds by use of descriptor pairs ReRe, SiSi=Ik or ReSi, SiRe = ul, respectively. However, these offer no advantages over the more graphic seqcis = Z or seqtrans = E usually employed. On the other hand, the expressions Ik and ul do appear to be particularly suitable Angew. Chem. IN. Ed. Engl. 21 (1982) 567-583 for specifying the steric course of asymmetric syntheses involving reactions between planar triligant atom centers, a suggestion which is dealt with in greater detail reflection-variant reflection-invariant __ ~ @ < @ I @ < @ I 1 accompanied by another enantiomorphic unit specifiable by descriptor S and vice versa. A reflection-variant stereogenic atom can conceivably be situated on a two-fold or three-fold axis of rotation. Such relatively rare cases will be discussed, with appropriate examples, in Section 6.3. It is clear that in a stereomodel every n-fold axis of rotation requires at least n stereogenic units having equal descriptors which lie outside this axis. Here the difference between hierarchical digraphs of cyclic and acyclic molecules should once again be emphasized. With the latter, in which all digraphs are derived from the same nondirected graph, the descriptors of all stereogenic atoms present are definitive-this is not the case with cyclic molecules. Whenever, for the sake of discussion, it is necessary to use such auxiliary descriptors we shall differentiate between these and the definitive descriptors by marking the former with the subscript 0. 5. Sequence Rules 5.1. Sequence and Assignment Rules 1966 The Sequence Rules (standard sub-rules) were formulated in 1966 as follows[’]: achiral ligands : A,B,C,D ...H...X; chiral ligands : F,G.. .; enantiomorphic Ligands F , q=F. A>B>C>O.. .>F>F>H.. .X Scheme 2. Descriptors of stereogenic units. g) For the sake of consistency one can use the reflectionvariant terms Lk and Ul for the descriptor pairs reRe, siSi, and reSi, siRe for the specification of “geometrically enantiomorphic” stereoisomers (see Section 6.4). Further to what was said earlier about the convention of vector directions one could equate descriptors P,p with the algebraic sign and M, m with the sign - . However, for historical reasons R , r, Re, re are equivalent to -, and S, s, Si, si to + : in 1956 the symbols R, S, r, and s were chosen so that most D-sugars and L-amino acids would be allocated descriptors R and S, respectively. In cases where stereomodels contain elements of symmetry it may be advisable to subject their descriptors to a test of symmetry consistency. Stereogenic units denoted by reflection-variant terms R or S can never lie in a symmetry plane. The latter can only accommodate units with reflection-invariant descriptors r or s. No tetrahedral stereogenic unit should ever coincide with a center of inversion. If the stereomodel contains a plane of symmetry or a center of inversion, every stereogenic unit in that model which can be specified by a reflection-variant descriptor R should be +, Angew. Chem. Int. Ed. Engl. 21 (1982) 567-583 (0) Nearer end of axis or side of plane precedes further (1) Higher atomic number precedes lower (2) Higher atomic mass number precedes lower (3) Seqcis precedes seqtruns (4)Like pair R , R or S,S precedes unlike pair R,S or S , R ; and M,M or P,P precedes M,P or P , M ; and R,M or S,P precedes R,P or S , M ; and M,R or P,S precedes M,S or P , R ; also r precedes s. ( 5 ) R precedes S ; and M precedes P. If it is possible to denote the order of precedence of the four ligands a > b > c > d present in a tetrahedral array by application of the Sequence Rules, then stereogenic units are assigned descriptors according to the “chirality rule’’: Among ligands of highest precedence the path of their sequence is followed from the preferred side of the model, that is, the side remote from the group of lowest precedence, and, depending on whether the path turns to right or left, the chirality unit will be assigned the chiral label R or S, or, if pseudoasymmetric, r or s. With a helical array the “helicity rule” applies: Depending on whether the identified helix is left- or right-handed, it is designated “minus” and marked M , or “plus” and marked P. Although both assignment rules can each be expressed in different ways‘301there is no reason for changing the original versions, which have found their way into elementary textbooks. It might be worth pointing out, however, that they are exchangeable. After having determined the rank 575 of proximal atoms a > b > c > d, one can determine and specify the stereogenic unit as a right or left helix according to the helicity rule. Alternatively one could construct a tetrahedron from four helically arranged points 1-2-34 and specify it according to the chirality rule. Between the descriptors thus obtained the following simple relationships apply: PuR; MctS;pc+r; and m u s (Fig. 16). P R S over the latter. The original precept in its abbreviated form, cis > trans, is still valid, but now these terms apply to the location of an atom or atom group of higher rank in relation to the core of a stereogenic unit, rather than to the configuration the double bonds themselves. The way this revised rule applies in the case of Figure 17 is shown by the adjacent hierarchical graph. M OH 0 \ /O 3-4 2-3 t I + I Fig. 16. Equivalent assignments of descriptors by the chirality and by the helicity rule. 5.2. Sequence Rules 1 and 2 In the majority of cases the relative rank of ligands is established on the basis of material differences, i. e. by application of rules 1 and 2. These constitute the solid basis on which the CIP system rests and there is no reason for revising them. 4'6' '5' 2 Fig. 17. Stereogenic atoms C- 1 and C-3 with geometrically distinguishable unsaturated ligands which cannot be specified using seqcis or seqtruns, respectively. Figure 18 should serve to demonstrate that if the modified rule 3 is used in cases where double bonds could be specified alternatively by seqcis or seqtrans, it would lead 5.3. Revision of Sequence Rule 3 In contrast there is a need, in view of more recent developments, for revision of rule 3, dealing as it does with certain of the geometrical differences of ligands. The following will differentiate between ligands which differ in cistrans isomerism due to planar tetraligant atoms or double bonds, and ligands which differ in cis-trans isomerism in rings. 5.3. I . cis-trans Isomers Associated with Double Bonds When two ligands, materially and topologically identical, differ in their geometry at double bonds, rule 3, as applied up till now, has assigned to first encountered double bonds descriptors seqcis =2 or seqtrans = E, respectively, followed by establishing precedence through the precept seqcis>seqtrans. When this rule was put forward, molecules in which assignment of seqcis and seqtrans is not possible, even though their stereogenic units contain ligands with double bonds differing in cis-trans isomerism, were unknown. A simple example is that shown in Figure 17. We therefore suggest the following minor modification of rule 3 in order to specify cases of this type: When two ligands (indistinguishable by rules 1 and 2) differ by one having the atom or the atom-group of the higher rank in a cis-position to the core of the stereogenic unit, and the other in a trans-position, then the former has precedence 576 Fig. 18. A stereogenic atom with two geometrically different unsaturated ligands, whose specification by the previous and by the revised rule 3 gives different descriptors (S and R., respectively). to a situation in which the previous and the modified rules lead to different descriptors. Hence, even though cases of molecules with stereogenic units whose ligands differ as a result of double bond isomerism are raref3'],and have not hitherto been specified using the CIP-system, we would suggest adding the subscript n (for new) for all descriptors assigned by the modified rule 3. 5.3.2. cis-trans Isomerism in Ring Compounds Here it is necessary to introduce a substantial change. In principle, cis-trans isomerism in ring compounds is threedimensional diastereomerism. The stereomodels of such diastereoisomers should reveal ligands with at least one pair of three-dimensional stereogenic units specifiable by descriptors such as R, S etc. The geometrical differences should be specifiable by either an unlike or like pair of descriptors, respectively. In other words, this type of diastereoisomerism ought to be specified using rule 4 as in the case of analogous acyclic molecules and not rule 3. Angew. Chem. Inr. Ed. Engl. 21 (1982) 567-583 Up to now it has frequently been possible to determine the rank of ligands by either rule 3 or rule 4. Any ambiguity had been forestalled by the requirement that each rule had to be applied exhaustively before proceeding to the next one. Nonetheless it seems unreasonable to use two overlapping rules for one and the same type of three-dimensional diastereoisomerism, while at the same time using rule 3 to specify both two- and three-dimensional diastereoisomerism. Apart from a point of principle there are good practical reasons for modifying rule 3. In the case of multi-membered, polycyclic, or spiro ring systems it is often not at all easy to ascertain (even using a computer) which ligands belonging to distant stereogenic atoms are in a cis- or a trans-position to each other; a point which is especially pertinent when one tries to find an answer to this question on the basis of structural coordinates determined by X-ray analysis. Unfortunately, and unavoidably, there are cases where descriptors assigned to stereogenic units by the new rule may differ from those established by rule 3 in its original form: to forestall misunderstanding, such descriptors of the “new” type should receive the subscript n. uated as like (I)or unlike (u). The first different pair determines the sequence of these ligands. Angew. Chem. Int. Ed. Engl. 21 (1982) 567-583 21 ’ \ :--s-z 2 X-El--R S-B-X \ s-s-Y I / I \ B-C-B / Ruuu Y-ff-S suu I < b) 5.4. Sequence Rule 4 Whereas the actual wording of this rule remains practically unchanged, in view of its applicability to the specification of cis-trans isomerism in cyclic molecules its general scope has been considerably extended. Hence it may be necessary to spell out more accurately how one should use it to arrive at an unambiguous specification. Before applying rule 4 it is useful to derive from the first hierarchical digraph a second one, in which stereogenic centers (or generally units) which had initially been specified using rules 1 to 3 are now replaced by descriptors R and S (or M and P) (cf. Fig. 19). One now systematically examines pairs of ligands containing two or more stereogenic units for geometrical differences arising from various alternative combinations of their descriptors. The comparison of such descriptor pairs should proceed in such a way that all relevant but no redundant information is used. This can be achieved by the following procedure based on general CIP principles: Before pairing, the descriptor chosen as first is that highest in rank according to rules 1 to 3. One now forms the descriptor pairs by pairing the one chosen as first in each ligand with one of the (n- 1) remaining descriptors in the order prescribed by the scheme shown in Figure 14. This is then followed by comparing corresponding pairs in both ligands. As soon as a difference is found, rule 4 is used in order to establish the sequence of ligands. The whole procedure is illustrated by examples in Figure 19a-c. In a) the “first” descriptor is the one found in a topologically preferred location, in b) it is the one seen in the highest ranked branch of the hierarchical digraph, and in c) it is the descriptor that occurs twice in the highest ranked triad. The descriptor thus established as first is now paired with other descriptors in the sequence of their order numbers (11, 21, 31, 111, 211 etc.), and the descriptor pairs thus formed are in turn eval- / ff-ff--X 2il 5-I37 S-ff- a-s’ El-ff \ I / / C-C-C-s-ff I \ -.f f - R Sfuuuu ff-m, I B-C-B Rulu Sulu ’ Ruul Suul Ru/I suuu = / @--S Ruuu S U / l Fig. 19. a) b) c) d) Descriptor assignment in stereogenic atoms whose ligands contain different descriptor pairs. The rationale of this procedure can be stated as follows: A complete graph whose n vertices represent the descriptors and whose edges represent the n(n - 1)/2 descriptor pairs can be unequivocally mapped onto a spanning treegraph whose root is the first descriptor. The (n- 1) edges of this spanning tree-graph, shown in Figure 19a as bold lines, contain all the relevant descriptor pairs. A special case is that of ligands containing enantiomorphic stereogenic units and consequently inverse descriptor pairs in positions of highest rank. Here one forms all relevant descriptor pairs using both the R- as well as the S-descriptor, after which one compares all pairs situated at the same rank level (Fig. 19d). The highest-ranked difference is then used for establishing sequence. Had only one of the two enantiomorphic ones (e.9.. R) been used as first de577 scriptor, this would have led to the evaluation of enantiomorphic Iigands as geometrically different. Figure 20 shows the specification of the six stereogenic atoms in (+)-inositol, as an example of sequence determination on the basis of differences between descriptor pairs, in a cyclic molecule. The procedure is shown in detail for carbons C-1 and C-2 with the aid of their hierarchical digraphs; the other four atoms can be specified in the same manner. As in the case of acyclic compounds one uses the first-encountered different descriptor pairs in order to evaluate the two branches of the bidentate ligand using rule 4. stereogenic atoms have been specified by applying rules I to 5 (Fig. 21a). The subrule of rule 4, r precedes s, can thus be applied only after rule 5 has been used to determine descriptors r or s, respectively. In order to keep to our precept that each rule be employed exhaustively before proceeding to the next one, we suggest that this subrule (r>s), even though based on a geometrical difference. become a second part of rule 5. H H R-r-S I R OHR I [ OH R H- 1 -R+R-I’-H ( H H--!+~-H I S H S ff-s-s S I H S 4 I R-r-S HO 5Rn ...._. 5 6 & ’SO H H OH 1 2 3 H OH OH H I I I HO HO 5 U H 6 I I OH H I I I 4 H H OH 1 2 3 I ..... OH 5 I U etc. Fig. 20. Descriptor assignment of stereogenic atoms in (+)-inositol. 5.5. Sequence Rule 5 Here, too, the wording of this rule remains unchanged but a few further remarks clarifying its use are necessary. After having failed to discover any geometrical differences between ligand pairs pertaining to stereogenic units containing descriptors, one proceeds to compare corresponding descriptors in two ligands. If they are inverse, then one uses those of the highest rank for determining sequence. A pair of enantiomorphic ligands together with two other ligands which are not enantiomorphic together constitute a “pseudoasymmetric” stereogenic unit, which is specified according to rule 5 using reflection-invariant descriptors r or s. It should be noted that a stereogenic unit containing two different pairs of enantiomorphic ligands (cf. 1321) is not pseudoasymmetric, but is a chirality element which has to be specified by the reflection-variant descriptors R or S. A special case is that of stereogenic units with ligands, whose sole difference is that they contain two different “pseudoasymmetric” stereogenic atoms. The CIP-system recognizes such chirality elements only after all the other 578 I R-S-S I I H S-C-S I 1 H Sn S1 o Ro I ..... I OHR-c-R R-r-S Ib ...._ HO HO b) H OH Ssn s I ff- s-s I H H ff-T-s H I R-S-s OH R - i - S la I H C-H I s - r - ~ I I H H S S C) d) Fig. 21. Graphs with descriptors assigned according to rule 5. The descriptor for the central stereogenic atom in case b) can be assigned only by subsequent reapplication of rule 4 ( / > u ) . It is thus not difficult to envisage structures such as that shown in Figure 21b, in which we meet with the following situation: topological differences engender geometrical differences, which in turn lead to new topological differences. It appears, however, that such compounds have not yet been prepared. Stereogenic units are conceivable[4b1which contain constitutionally equivalent ligands, differing only in that one of them comprises a chiral and the other a pseudoasymmetric stereogenic unit (Fig. 21c). A ligand with a chiral or pseudoasymmetric stereogenic unit could also be juxtaposed to a constitionally equivalent ligand without the corresponding stereogenic unit (Fig. 21 d). In such cases we propose that the chiral stereogenic unit should preceed the pseudoasymmetric one, and the ligands with a chiral or pseudoasymmetric unit should preceed the one without a corresponding stereogenic unit. 5.6. Summary of Revised Sequence Rules If, as we have recommended, specification of chirality planes and chirality axes is carried out on the basis of preferred helical domains, rule 0 becomes superfluous. Rules 1 and 2 and their application remain unchanged. Rule 3 should henceforth be restricted to ligands which differ in cis-trans isomerism of planar tetraligant atoms or double bonds. It should then read as follows: When two ligands differ only in that one has an atom or atom-group of higher rank in a cis-, and the other in a trans-position to the core of a stereogenic unit, then preference is given to the former. Revised rule 4 is as follows: When two ligands have different descriptor pairs, then the one with the first-chosen Angew. Chem. Int. Ed. Engl. 21 11982) 567-583 =m like descriptor-pair has priority over one with a corresponding unlike descriptor-pair. Like descriptor-pairs are: R R , SS, RRe, SSi, ReRe, SiSi, M M , and PP, and also by corollary R M , SP, ReM. and SIP. Unlike pairs are: RS, ReSi, SRe, ReSi, M P ; and by corollary RP, S M , Rep, and SIM. The rule stating that a ligand with descriptor r has preference over one with descriptor s is used as rule 5b, since it will only be used following rule 5a. Rule 5a reads exactly as the original rule 5 : A ligand with descriptor R or M has priority over its enantiomorph with descriptor S or P. 4 6 6 6. Parerga and Paralipomena In the preceding sections we have endeavoured to describe the revised CIP-system in concise form, and to this end we have used only simple and lucid examples to illustrate our arguments. The purpose of this section is to show that the revised system also lends itself to the treatment of more complicated cases, in particular those which various workers in this field have considered unspecifiable. i Fig. 23. Hierarchical digraph of C-l in cuneane. 6.2. Compounds with Hitherto Unspecifiable Stereogenic Atoms 6.2.1. Achiral Cyclic Stereoisomers 6.1. The “Finiteness” of the Specification Process In 1966“’ a statement, supported by two examples, was published to the effect that examination using the Sequence Rules must be terminated when the specifiable chirality center has been reached. In spite of this Schubert and Ugi stated in 1979 with reference to the molecule shown in Figure 22Is1 that “no matter how many iteration steps are performed it is impossible to put the ligands into order. Here the CIP-Sequence Rule fails”. They gave another four examples where, in their view, ligands could not be put in sequence and came to the devastating conclusion that the CIP-system “is fundamentally incapable of ordering ligands”. & 6 A systematic utilization of hierarchical digraphs of cyclic compounds makes it possible to specify “pseudoasymmetric” stereogenic units, which up to now required the use of the cis- and trans-descriptors. Well-known examples are the stereogenic atoms in 1,3-disubstituted cyclobutanes, in cis- and in trans-decalin, in all-cis- and in alltrans-inositols, and in many of their homologues and analogues. For example, let us consider stereogenic atoms C-1 and C-2 in cis-1,3-cyclobutanediol (Fig. 24), which the unreOH 0 1-4-3-2-1-4-3-2I 0 I I I 5 0 I H n .I H Ro 5n SO 1 1 OH OH Fig. 22. Hierarchical digraph of C-l in tricyclo-[5,1,0,0”5]-octane H 0 n I -4-3-2-1 I I I H 0 RO f” % 0 1-4-3-2-1 The hierarchical digraphs of two of the structures used as a negative example (Figs. 22 and 23) demonstrate that this conclusion is completely unwarranted; and the remaining three structures quoted by them can be specified in an analogous manner. Angew. Chem. Inr. Ed. Engl. 21 (1982) 567-583 I I Fig. 24. Hierarchical digraphs of C-1 in diastereomeric cyclobutane-1,3diols. 579 vised CIP-system could not specify. In the hierarchical digraph of C-1 we now see that C-3 is a specifiable stereogenic atom in both of the branches corresponding to the ring, In the left branch it is assigned descriptor Ro and in the right descriptor So. Hence C-1 is a pseudoasymmetric 1! 6.2.2. 2.6-Adamantanediol In this molecule we find two stereogenic atoms which until now could not be specified. This particular example shows how one can establish the rank of ligands in the case of a highly symmetrical (Td) polycyclic framework. Since obviously 0 > C, C > H, what one has to tackle is the problem of the proximal ligand atom pairs (C-1, C-3) 10 H 7-6-5 1 I I 1 -C4--S-C-l I 1 -C4-6-C4-1 I I I H H H RO *n SO H H 1 5-6-7 I H I -C4-6-C4- 1 -C4-6-C4--l I I H 1 I I 1 Fig. 25. Hierarchical digraphs of C-1 in diastereomeric decalins. atom, which by rule 5 is specified by descriptors. The fact that C-3 has different descriptors in each branch demonstrates that this atom is topographically different (enantiomorphic) with respect to C-1. These C-3 descriptors are auxiliaries which do not appear in the final specification. The definitive descriptor of C-3 has to be ascertained by examining its own hierarchical digraph; and this shows that for this atom, too, the descriptor is s, in accord with the Cz point symmetry of the molecule as a whole. By the same procedure one obtains descriptors lr, 3r for trans-1,3cyclobutanediol (Fig. 24), Is, 6s for cis-decalin lr, 6r for trans-decalin (Fig. 25), and lr, 2r, 3r, 4r, 5r, 6r for all-transinositol (Fig. 26). a 2 ? ' ?H c4-$-9 fi a s b b 4-&9c ti ti so H z, 6 H OH H .....++$HO H 6 1 S, n' OH a a s 9 c 8-7-10 b8-t-lOc b k k so R, a a HO c7-65 b ? b 7-6-5c A H Po so 2 R, Fig. 26. Hierarchical digraph of C-1 in all-trans-inositol. 580 / Fig. 27. Hierarchical digraphs and auxiliary descriptors of C-2 in (S)-2,6-adamantanediol. Angew. Chem. Int. Ed. Engl. 21 (1982) S47-583 at C-2 and (C-5, C-7) at C-6. Figure 27a shows the hierarchical digraph of stereogenic carbon atom 2. Ligands at C1 and C-3 exhibit no constitutional differences and they must be different geometrically. On the basis of constitutional differences one first assigns auxiliary descriptors to stereogenic atoms C-5, C-7, and C-6. It then follows from Figure 27b that the ligand at C-1 contains two like (0 auxiliary descriptor pairs, and that at C-3 two unlike (u) ones, from which it follows that C-1 >C-3 and the descriptor is 2 s . I n accordance with the molecule's C2-symmetry one then arrives at the descriptor 6s. 6.2.3. R. S. Cahn 's Cycfobutane Derivatives Among molecules with mutually interdependent stereogenic atoms of different type the four test cases suggested by Cahn (cf. [7.331) (Fig. 28) deserve special mention. After Sn and then evaluating the others through their topological distance from this atom on the hierarchical digraph. The examples in Figure 29a-c show how the ligands can be thus ranked clearly and simply. The chiral molecule with point symmetry D2 has a stereogenic central atom with four rotationally equivalent proximal atoms; the chiral molecule with point symmetry C-3 has three such proximal atoms. In the chiral molecule with point symmetry C, we find a stereogenic central atom with two rotationally equivalent proximal atom pairs. The fourth example in Figure 29d is of interest since it deals with an achiral molecule with &-point symmetry. The central atom is not stereogenic. Going through the above exercise using atoms C-1 and C-7 as reference atoms one arrives at a sequence leading to descriptor R, and using atoms C-4 and C-11 as reference one obtains descriptor S. These descriptors cancel each other out. This result Jn Fig. 28. Descriptors of the four diastereomeric cyclobutane derivatives. Hierarchical digraphs of stereogenic atoms in C, diastereoisomer. constructing the requisite hierarchical digraphs it emerges that in all four examples the stereogenic atoms are all specifiable using symmetry-concordant descriptors ; this is exemplified in extenso by digraphs with the stereoisomer having C, point symmetry. 6.3. Ligands of Rotationally Symmetric Stereogenic Atoms which are Topologically Distinguishable Proximal atoms in a polydentate ligand of a tetrahedral stereogenic atom need not necessarily be different; they may be rotationally equivalent and yet be distinguishable by their location relative to each other within the polydentate ligand. As demonstrated in 1966 such stereogenic atoms can be specified by arbitrarily allocating highest rank to one of the rotationally equivalent proximal atoms Angew. Chem. Inr. Ed. Engl. 21 (1982) 567-583 has been arrived at merely by consideration of the relative topological ranking of proximal atoms discernable from the hierarchical digraph, without any foreknowledge of the symmetry of the molecule. This should serve to illustrate the requirement that for determining order of sequence based on relative topological differences all proximal atoms must be used as reference atoms. The ligand sequences thus obtained lead to pairs of the same descriptor only in the case of chiral molecules, whereas with achiral molecules one obtains pairs of enantiomorphic descriptors. This criterion of topological differentiation of ligand atoms attached to a central stereogenic atom in relation to one chosen freely and arbitrarily from the rank-highest equivalent (homotopic) among them can be used to specify stereogenic atoms in many different types of rotation-symmetric molecules, such as that shown in Figure 30L34'and 58 1 8 sg o\ 8 c3 0 2 its many stereoisomers and analogues. For specifying C-1 one can use either sequence a , > a 2 > b l > b 2 or a2> a, > b2> b,. Both sequences will lead to descriptor R for this and consequently for the other four stereogenic rotationally equivalent atoms. / 8 s, C2 6.4. Geometrical Enantiomorphism D2: D 4 \? I l Lyle and Lyle[3s1have used the term “geometrically enantiomorphic stereoisomers” for enantiomers with constitution (A,B)X=Y(F,F), where A and B are two different chiral ligands, and F and F represent an enantiomorphic ligand-pair. 7 I 6 I 3 3 5 \I/ / 7 a-+-m-ii-a,+g 4 Fig. 30. A molecule with C , axis. Hirschrnann and H a n ~ o n [have ~ ] suggested using the reflection-variant descriptors seqCis and seqTrans (note capitals!) for such enantiomers. Our example in Figure 31 shows that the enantiomer on the right can be specified using the “like” descriptor pairs reRe or siSi, and that on the left by the “unlike” pairs siRe or reSi. Since these are reflection-variant descriptor pairs, the logical abbreviations for these are Lk and Ul. respectively. 0 C,: I I C2: 2 4 3 I / H 5-6-7 07-4-5 I / \ 6 I 8 5I 1 2 cn, n3c re I 8 7 i’ I\ ‘R I U/ i b) m I ‘S ‘ U Lk Fig. 31. Specification of “geometrically enantiomorphic” stereoisomers. C R and Cs as in Fig. 28. S, : t 2 I 5 \I/ 3 4 8- 9-100-11- 12-0 10-11-12 Ot7<8 6-5-4-3-2-1 A? I \ I 8 I 12 I E l \ 2- m3-2 / 1 9 11 11 7 ‘S C) 7 5 5 8 3 - 2 4 4 *\P 6 4 f Y /8-g-10 lo \6-5-@ 1-7-8 /n 9 11 11 I 10 / 7 8 I 7 I\ I 12 1 I I’ 6 2 I 10 I Fig. 29. Hierarchical digraphs of four molecules with rotation-symmetric topologically distinguishable ligands. 582 Angew. Chem. In:. Ed. Engl. .?I (1982) 567-583 7. Epilogue An ancient Chinese proverb states that a picture can often obviate a thousand words. One can, however, obviate thousands of pictures by means of a right word (descriptor) at the right place and a left word at the left place. Received: May 10, 1982 [A 422 IE] German version: Angew. Chem. 94 (1982) 614 We are greatly indebted to Professor H . J . Eli Loewenthal, Haifa, for the English translation of the German manuscript. [I] R. S. Cahn, C. K. Ingold, V. Prelog, Angew. Chem. 78 (1966) 413; Angew. Chem. Int. Ed. Engl. 5 (1966) 385 and previous communications [2, 31. [2] R. S. Cahn, C. K. Ingold, V. Prelog, Experientia I2 (1956) 81. [3] R. S . Cahn, C. K. Ingold, J . Chem. SOC.1951, 612. [4] a) E. F. Meyer, J . Chem. Educ. 55 (1978) 780; J. Comput. Chem. I (1980) 229; b) another computer program for assignment of CIP-descriptors to stereomodels has been developed by R. Custer, lnstitut fur Organische Chemie der Universitlt Zurich (personal communication). [5] K. R. Hanson, J. Am. Chem. SOC.88 (1966) 2731. 161 V. Prelog, G. Helmchen, Helu. Chim. Acta 55 (1972) 2581. 171 H. Hirschmann, K. R. Hanson, Tetrahedron 30 (1974) 3649. [S] W. Schubert, I. Ugi, Chimia 33 (1979) 183. [9] Concerning the exact definition of the terms geometry and topography KIein [lo] wrote the following comments, which have already been quoted in [6] and which, in view of their importance for understanding the subject, we requote (translated from the original German): “Geometry deals only with those relationships between coordinates which remain unaltered during substitution operations such as mentioned under 1 (i. e. parallel displacements, rotation about the coordinate origin, reflection and similarity transformations). In other words, geometry is the invariant theory of these operations. On the other hand, all non-invariant relationships between coordinates, e. g . the statement that a certain point has coordinates 2,5,3, refer to a system of coordinates which has been fixed once and for all-they belong to a science which individualizes each point and deals with the properties of each separately, namely the science of topography ...”. It follows from this that chirality (onentability in Euclidean space) of a figure is a geometrical property, whereas chirality sense (the orientation of that figure and its algebraic sign) is a topographical one. [lo] F. Klein: Elementarmathematik uon hoherem Standpunkt aus, 2. ed., Springer-Verlag, Berlin 1925 (reprint 1968), p. 141. [ I I ] Although in principle. static stereochemistry could dispense with the use of the rather ill-defined term chemical bond, we would not consider such a move as appropriate and agree with the pointed remarks made by a mathematician, H. Weyl (121 who writes (translated from original German): “one should not take arbitrary relational representations such as valence diagrams too seriously even though they have their use in serving as a rough guide through a seemingly chaotic accumulation of facts. One cannot expect a rough sketch purporting to represent reality to contain all possible shades of that reality. Nonetheless the sketcher should have the courage of his convictions and draw the lines firmly”. Angew. Chem. Int. Ed. Engl. 21 (1982) 567-583 [I21 H. Weyl: Philosophie der Mathematik und NarunvissenschaJt. 4th ed., Oldenbourg, Miinchen, 1976, p. 352. [I31 In order to stress the difference between molecules and models we restrict the expressions “enantiorner” and “diastereomer” to molecules and compounds only (cf. [6]). When referring to geometric and topographic interrelationships between models, ligands, or other objects we use the terms “enantiomorphic” and “diastereomorphic” (cf. (141). [I41 K. R. Hanson, Ann. Reu. Eiochem. 45 (1976) 307. [IS] The CIP-system does not take into account diastereomers whose models are differentiated only by the magnitude of their internal coordinates (but not by their algebraic sign). Stable diastereomers of this type are exemplified by “cogwheel” stereoisomers [16]. These can be specified by using the descriptors sp, sc, ac, and ap, proposed by Klyne and plelog [17], which indicate the approximate magnitude of torsion angles. (16) M. Oki, Angew. Chem. 88 (1976) 67: Angew. Chem. Int. Ed. Engl. I5 (1976) 87. [I71 W. Klyne, V. Prelog, Experientia 16 (1960) 521. [I81 A. F. Mtibius: Der barycentrische Cafcut. Gesammelte Werke, Vol. 1, Leipzig 1885. [I91 The algebraic sign of this volume can be defined as that of the pseudoscalar product of the three bond vectors V = . ? . y x f i in a right coordinate system. (20) H. Gerlach, Habilitationsschrift, ETH Zurich 197 I . [21] V. Prelog, Pure Appl. Chem. 25 (1971) 465. (221 V. Prelog, Science 193 (1976) 17. (231 K. Mislow, M. Raban, Top. in Sfereorhem. I (1967) 1. 1241 In a pamphlet issued by Chemical Abstracts Service (A New General System for the Naming of Stereoisomers. Columbus, Ohio, 1953, p. 2) G. E. McCasland suggested the following definitions of a stereogenic atom: “a) An atom (usually carbon) of such nature and bearing groups of such nature that it can have two different configurations. b) An atom bearing several groups of such nature that an interchange of any two groups will produce an isomer (stereoisomer).” I251 This kind of stereoisomerism is usually denoted by the too general and hence misleading term “geometrical isomerism”. In fact every diastereoisomerism is a geometrical isomerism. (261 J . H. uan’t HoJJ the originator of the model of the “asymmetric atom”, at first placed the atoms and atom groups proximal to the central atom on the faces of a tetrahedron (cf. (271). This is feasible because replacing the vertices of a tetrahedron by its faces and vice Versa produces an “inverse” tetrahedron. At a later stage uan’t Ho/f relinquished this original idea; much later still it was taken up again as the basis of modern spacefilling models. (271 0. Bertrand Ramsay: Sfereochemistrv, Heyden & Sons, London 1981, p. 84. [28] G. L. Lemidre, F. C. Alderweireldt, J. Org. Chem. 45 (1980) 4175. 129) D. Seebach, V. Prelog, Angew. Chem., in press. 1301 K. Freudenberg, Natunvissenschaften 64 (1977) 338. [31] R. Riemschneider, K. Brendel, J. Takei, Liebigs Ann. Chem. 665 (1963) 43 and previous papers in this series: J. Gray Dinwiddie, Jr., H. M. White, J. Org. Chem. 33 (1968) 4309. (321 A. Werner: Lehrbuch der Stereochemie, Gustav Fischer, Jena 1904, p. 29. (331 H. Hirschmann, K. R. Hanson, J . Org. Chem. 36 (1971) 3293. 1341 We are indebted for this example to Dr. 0. Weissbach, Beilstein-Institut, Frankfurt am Main. I351 a) R. E. Lyle, G. G. Lyle, J. Org. Chem. 22 (1957) 856; b) G. G. Lyle, E. T. Pelosi, J. Am. Chem. SOC.88 (1966) 5276. 583

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